Sampling-based planners (SBPs) operate based on growing a tree or graph of sample points \(\mathbf {x}_i\)  within a sample space \(\mathcal {X}_{free}\)  and have been applied to a large number of robotic motion planning problems [1]}. A key advantage of SBPs is that difficult constraints, like collision-checking, can be explicitly checked during exploration of the state space. This framework uses kino-RRT, a variant of the popular rapidly exploring random tree (RRT) algorithm. kino-RRT includes the robot dynamics and is a good candidate for a long-horizon planner when numerical optimization-based planning becomes impractical [2]}. The reader is referred to Karaman for implementation specifics [3]}. Utilizing the advantage of a direct collision checking module, one may use ellipsoidal constraints for instance in order to perform simple collision checking; such constraints are common for space robotics motion planning scenarios [4]}. The result of this initial long-horizon planning is a path, \(\mathcal {P}_g\) , of \(\mathbf {x}_{0:{N_g}} \in \mathcal {X}_{free}\) , where each node obeys \(\mathbf {x}_{k+1} = f(\mathbf {x}_k, \mathbf {u}_k)\)  and any additional enforced constraints. Dynamics propagation is typically accomplished using a set of representative \(\textit {motion primitives}\) . The kino-RRT is represented as the green solid line in Fig. REF , with motion primitive actions connecting adjacent waypoints. Global planning is nominally performed only once prior to motion, but online recomputation is enabled by reasonable solve times relative to the dynamics of interest (e.g., a few seconds for robotic free-flyers).
